I am getting started on HW 3 and have run into some confusion on the first problem. Can anyone steer me in the right direction... Here's what I was thinking: the 200 kHz that is mentioned in the problem is fs. In part a it says to derive expressions for Voc and Isc... I am assuming that Voc will be (4/pi)*Vg * H_inf(jws) and Isc = I/sqrt(1-(V/Voc)^2), where I=Vnom/Rnom and V = Vnom. The issue that I am finding is that I am not seeing how to get an F term in the expressions, any hints?
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Should I use H(s) instead? Also, when he says Cs||Cp is that the same as 1/(Cp + Cs) when it is simplified?
Cs||Cp=Cs*Cp/(Cs+Cp).
Don't think Rnorm will be used in part (a).
Use only the source voltage, tank elements, open/shorted load, and normalized switching frequency F=fs/finfinity.
The derivation is a little awkward.
So you suggest Isc = Vs1/(Ls + 1/Cs*s) instead of what I had proposed? I got Voc in terms of n and F (no R_inf term)... I'll have to work on Isc a bit to get anything more than gobbledegook... are you getting an R_inf term in Voc?
R_inf only appears in Isc result.
If you use Vnom at all, it is rms, I know that always trips me up.
I'm feeling pretty silly, but I still can't get an R_inf term in Isc in either method... If I use Isc = I/sqrt(1-(Vnom,pk/Voc)^2) I get an Rnom term from the relationship of I = Vnom/Rnom. If I just short the load, then I get Isc = Vs1/(Ls + 1/Cs*s) which doesn't even have a Cp term in it. (Isc = (4Vg*Cs*s)/(pi*LCs*s^2 +1) Where am I going wrong?
Is there some relationship between Rnom and R_inf?
I just finished up Voc, but how are you handling the relationship of Cs to Cp? In my Voc expression, I originally started with the note in the HW assignment that n=1 and Cs=Cp, and I got something kind of funky. When I left n in and instead used the relationship n = Cs/Cp, I got a much nicer answer. I'll post something again when I get through my own calculations.
Luke,
I left n = Cs/Cp and ended up with an n / (n+1) term and basically the same equation derived in class... Let me know if you figure out Isc.
So what I'm struggling with is what exactly Rinf is. There is the relationship Isc = ||Hin||*||vs||/||Zo0||, and I'm inclined to believe that ||Zo0|| is somehow Rinf, but I am not having much luck in my derivation.
I am also struggling with it... I've been monkeying around with Zio, Zoo, Ziinf and Zoinf to see if I can get an expression that is the same as Rinf, but to no avail.
Luke, using the Isc equation you gave, it reduces to simply Vs1/||Xs|| as Olga mentions earlier.
After that, I'm stuck too. I think I'm on the right track, but haven't quite been able to work out all the kinks. I'm trying to replace the L in the equation with R_inf/w_inf,which gets fairly close. I'm left with all the correct terms, except for one additional C_s term.
Maybe you will have better luck?
Hi Carissa,
Indeed you are getting close. Just express Cs in R_inf, w_inf and n and you should be there.
Regards,
Toby
Eureka! So After following Carissa's line of thought, I found a way to get rid of Cs by manipulation of R_inf and w_inf, with the substitution of n*C_p = C_s.
All,
Thanks for the discussion, I was finally able to come up with an answer... and it looks like I will be using similar methods on 19.9 :)
Thanks Toby and Luke-
Four pages of algebraic scratches turned nicely into two lines. I think I was just stuck in a rut.
Hi everyone,
I'm going back to my problems for double-checking my answer, and it seems I had made an error on 19.6. Following Carissa's and Luke's thoughts, I solved for L=R_inf/w_inf and Cs=(R_inf*w_inf)/(1+n).
Plug in these two and I get a the terms as a function of R_inf & F, but I still have a term of w_inf that I can't get rid off. The problem seems to imply the answer should be Isc(n, Vg, R_inf, F), but I can't get rid of w_inf after doing some algebraic manipulation.
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